It was just five days after Boris Johnson had entered Downing Street when the six-member Brexit “war cabinet” met for the first time to set out a strategy for abolishing the backstop.

Known as the Exit Strategy or “XS” committee, it comprised Boris Johnson and five key cabinet ministers involved in delivering Brexit “do or die”.

According to highly placed sources, the meeting on July 29 discussed the diplomatic and tactical approach to getting rid of the backstop.

The plan, backed by David Frost, Mr Johnson’s Europe adviser, was to “run down the clock” with the EU closer and closer to the no-deal cliff edge. Senior sources say the strategy was adopted as formal policy, raising the question in Whitehall and Brussels of whether the government was actually serious about reaching a deal.

Mr Johnson spoke publicly about the “abundant” technical fixes for the Border and said “no deal” was a “million-to-one”, but in private he got very different messages.

At a follow-up meeting on August 1 to discuss what the strategy would mean in practice, Mr Johnson insisted again the entire backstop must go, but he was confronted by Attorney General Geoffrey Cox, who argued for potential compromises on the backstop that might be negotiable with the EU, – such as a time-limit or a unilateral exit clause – but the options were ruled out by the prime minister.

Sources say Mr Cox told Mr Johnson it was a “complete fantasy” to think the EU would drop the backstop.

With all the routes to a backstop compromise apparently shut down, Tory backbenchers fretting about the apparently rising risk of no deal were told by No 10 that “back channels” were being opened to the EU, but in truth there were no substantive negotiations.

On both sides, despite talk about exploring “alternative arrangements”, no real negotiations were taking place. In private strategy meetings, Dominic Cummings, the feared Leave campaign strategist appointed as Mr Johnson’s special political adviser, was frank, openly describing the EU negotiation as “a sham”, according to two sources.

A senior EU diplomat did not rule out Mr Johnson “doing a Trump” and accepting a small concession on the backstop which he could then describe as a tremendous victory but conceded it was now “hard to see” how this would ever garner a majority in Westminster.

For all the talk of solving the Border issue, no detailed or technical proposals were drawn up or put forward by the British side, multiple informed sources said. There is, nominally, a “legal text” for a new backstop but according to sources familiar with the document, it “took about half an hour” to produce and was essentially the old backstop “with all the important provisions crossed out”.

An EU source, with knowledge of the talks process, said: “The ball is in their court but we haven’t seen any detailed proposals and we don’t expect to see any until very late.”

Despite this, government ministers continued to profess optimism that a deal was possible, with Michael Gove, the no-deal chief, claiming that EU leaders were “shifting”.

This was in sharp contrast to an article by Michel Barnier the same day, which made clear the EU’s parameters for a deal were exactly the same: any alternative to the backstop must preserve the integrity of the EU single market and keep the Border “fully open”.

Given Mr Johnson’s position that all of the UK must leave the EU, the single market and customs union, it now appeared both no deal and a deal on that basis would lead to a disruptive trade border in Ireland. “There is no incentive for Ireland to move,” a third source added. Talk of Northern Ireland aligning on EU agricultural “SPS” regulations was floated to give the appearance of progress.

In any event, even agreeing to align with agricultural regulations addresses only “about 30pc” of issues at the Border, according to both EU and UK trade experts. This might be why at a meeting of the XS committee on August 27, Mr Frost reminded the cabinet of the decision to “run down the clock” and keep up the appearance of activity, which he said was “important for both process and domestic handling reasons”.

“All the emphasis and strategy is on managing the fears of backbenchers that we are heading to a ‘no deal’ – not actually on delivering a workable alternative to the backstop,” adds the source. At the same time, Mr Frost suggested formally opening a “no-deal mitigation” track that would run in “parallel” with efforts to negotiate an alternative to the backstop, further laying the groundwork for no deal: this despite Mr Barnier repeating there would be no “mini-deals”.

Even so Whitehall sources report much current industry is centred on drafting potential mini-deals that the government still “hopes” the EU will accept if it comes to no deal.

“They may talk about a deal but they know there is no time or political space to get one,” the first source said, “and nothing that is happening behind the scenes suggests otherwise.”